Transcript Using Number Lines - Lancashire Grid for Learning

Welcome to our
Maths Workshop
Primary School
Adult attitude to maths
Jenny:
‘My first thoughts of mathematics are
fear, not being able to do it and
feeling inferior.’
DfEE 1999 (10 years ago!)
‘Parents who are confident about
maths tend to have children who are
also confident, and these children
are ready to tackle and assimilate
new ideas in a way that is impossible
for children who feel uncertain
about, or even fear, maths.’
I find it much
easier if I have
some help at
home!
78 – 12?
How do you
work out….
20 - 6
74 – 57?
Lancashire Mathematics Team
20-6
14
15
20
78 - 12
66
66
78
68
76
78
74 - 57
57
57
60
74
67
74
Subtraction with
decimals on a number line
The many uses of a
number line
Imagine:
A similar situation where the pupils are
finding Problem solving with decimals
(money and time) difficult to access.
The train is due to arrive at 6.45am
but is 37 minutes late. What time
does it arrive?
How might a number line help?
Addition - Number lines
Are frequently used in each year group and
provide children with a very visual method
of calculation
• 15 + 8 =
• 29 + 23 =
Can you get from a starting number to 100 in
3 hops?
•
27 + ? = 100
•
48 + ? = 100
•
2 + ? = 100
Number lines can help with
estimating
• Where would 660 be on this number line?
(demonstration)
600--------------------------------------700
• Where would 310 be on this number line?
240--------------------------------------360
I told you to use a
number line!
Have a go!
• 22 – 5 =
• 145 – 94 =
• The bus is due to arrive at 7.35am
but is 46 minutes late. What time
does it arrive?
• Sally wants to buy a CD that costs
£15.60. She only has £13.45. How
much more money does Sally need to
buy the CD?
A number line is
just a ‘picture’ of
how we work out
some calculations
in our heads!
Addition & Subtraction
• Using number lines:
– We add by ‘counting on’
– We subtract by either ‘counting on’ or ..
– ‘counting back’ depending on the
numbers involved
– We also subtract by finding the
‘difference’
Guess the calculation…
17 + 3 = 20
Addition using a ‘compact’
method
No ‘Carrying’
4 1
+ 2 6
6 7
‘Carrying’
4 7
+ 7 6
1 2 3
1
1
Add up
If the number in each circle is the sum of
the two below it, what is the top number?
6
5
8
4
Add up
If the number in each circle is the sum of
the two below it, what is the top number?
36
15 21
6 9 12
5 1 8 4
Subtraction using a
‘compact’ method
• By decomposition
• Uses children’s understanding of the
number system
83 – 26
70
-
80
20
50



13
6
7
= 57
Dart board game – regrouping
and combining numbers
5
1
7
2
3
6
4
8
15
Morecambe and Wise
I’m playing all the right notes!
Just not in the right order!!
Decimal trails – you can use
a calculator to help
This game has immense value in different ways.
It can be differentiated and used for fractions
or percentages as well as simplified to be used
for whole numbers.
As a team: Start at decimal hound’s nose 0.5 you
have to make your way to each of the six
houses (Watch out for Mad Mansion – it’s
hard!). Write down your routes as you will
need to read them out
First team to finish wins
Multiplication
3 x 7
0
7
14
21
0
7
14
21
How many???
Grid method of multiplication
10
6
60
3
18
60 + 18 = 78
so 6 x 13 = 78
A vertically expanded method links into the
grid method and is a good way of moving
children on to compacted methods.
38
x7
210 (30x7)
56 ( 8x7)
266
38
x7
266
2 5
X
7
30
8
210
56
=266
BINGO!
• Yes it’s ‘clickety click’ twenty six (or
something like that!)
• BINGO is great for developing quick
mathematical skills.
• It can be used in a variety of ways.
• So lets have a go at 6, 7, 8, 9, 11 and
12x table Bingo.
• Eyes down…
Inverse – Multiplication
and Division
• We use times tables facts to help us.
23 ÷ 6
Same sum …
?r1
33 ÷ 4 = 8
12
7
3
6
5
4
8
8 remainder 1
I just can’t get
the hang of
this ‘chunking’ !
Chunking (Division)
79 ÷8
8 79
- 8
71
- 16
55
- 24
31
- 24
7
(1 x 8)
(2x8)
(3x8)
(3x8)
9 remainder 7
Division by ‘chunking’ or
‘lots of’
16
132
Gozinto
Equipment: Game board, 2 dice, 2 colours of
counters, multiplication grid
Play in 2’s, 3’s 4’s (have a judge who’s job is
to check responses on the multiplication
grid)
Rules: Throw the two dice and total up the
two numbers (e.g. 5 and 3 = 8). Find a
multiple of 8 on the board (e.g. 32) and
place a counter on it. The winner is the
one with the most numbers covered
36
99
32
40
18
35
42
84
33
56
66
20
54
63
10
55
36
22
50
48
27
28
12
24
60
44
45
77
30
96
21
40
72
49
11
64
48
88
30
Lancashire Mathematics Centre
Key messages
• Children need to develop skills such as
counting, partitioning and recombining
numbers
• They need to build an awareness of the
number system, value of numbers and
number relationships
• They need to recall facts such as halving
and doubling, number bonds and
multiplication facts
• From all of these they learn to construct
strategies that they can apply in many
different areas
Thank you for attending
tonight’s workshop